View photos Members of Iraqi police forces celebrate on a street on June 27, 2016 in western Fallujah, 50 kilometres (30 miles) from the Iraqi capital Baghdad, after Iraqi forces retook the embattled city from the Islamic State group (AFP Photo/Haidar Mohammed Ali)

Shiite militiamen are widely feared by Iraqi Sunnis, who worry they will carry out reprisal attacks as the country's forces battle to retake areas seized by IS, which overran swathes of territory in 2014.

Their presence inside Fallujah -- which Iraq announced Sunday was fully under government control -- was opposed by some Sunni politicians.

But while abuses including summary executions by militiamen -- who fall under an umbrella organisation known as the Hashed al-Shaabi, or Popular Mobilisation forces -- have been reported in areas near Fallujah, similar accounts have not emerged from inside the city itself.

And with Baghdad eyeing Mosul, the next target in its anti-IS campaign, the close cooperation between some militiamen and security forces in Fallujah may help them push for a similar role in the battle for Iraq's last jihadist-held city.

"We participated in liberating the city," Hadi al-Ameri, the commander of the powerful Iran-backed Badr militia, said in Fallujah.

He said the participation was not major, with around 1,500 militiamen fighting "side by side" with federal police and the interior ministry's rapid response forces, which along with the country's elite counter-terrorism service played the main role in the battle inside Fallujah.

Abu Hanan al-Kinaani, the commander of Badr's 4th Brigade, also said the group's fighters battled alongside interior ministry forces in various areas of Fallujah.

The involvement of the paramilitaries inside Fallujah contradicted earlier assurances that they would remain outside the city.

Ameri himself had previously said that "we will not enter Fallujah" and that their mission was to surround it.

Brigadier General Yahya Rasool, the spokesman for Iraq's Joint Operations Command, denied having information about the presence of Hashed fighters in the city and said that plan was for them to remain outside it.

"The mission of the Hashed al-Shaabi was to support the police and army units, and tighten the noose around Fallujah," he said.

- Graffiti, flags -

Asked about Hashed forces in Fallujah and whether Prime Minister Haider al-Abadi, the commander-in-chief of Iraq's armed forces, had requested their involvement, his spokesman Saad al-Hadithi declined to comment.

Ameri insisted that there had been no prohibition on the militiamen entering Fallujah, and said that those who were against it were protecting IS.

"I will send them black clothes" to mourn the government's recapture of Fallujah, he joked.

Ameri said that Hashed forces had voluntarily waited to enter the city until after civilians had departed out of concern for their safety.

While the involvement of Hashed forces in the city during the operation was relatively discreet, their presence is now far more open.

The names of Badr units are spray-painted on walls and buildings in Fallujah, and the group's flags fly at various points.

"This neighbourhood was liberated by the heroes of Badr," a message on one wall says.

A number of vehicles in the city, including an American armoured personnel carrier and a Humvee, are marked as belonging to Badr, and some bear Ameri's picture.

Badr's presence is the most conspicuous, but other Hashed groups were also said to have taken part in fighting inside the city.

Interior ministry and Badr commanders both said that Hashed al-Shaabi fighters worked closely with the federal police and rapid response forces during the Fallujah battle -- an arrangement that would mean they were more directly under government control than in some earlier anti-IS operations.

Such cooperation is likely aided by the fact that Interior Minister Mohammed Ghabban is himself a Badr leader, and could give the group's forces a leg up in navigating the process of what will happen to the Hashed after the war against IS.

Hashed fighters worked with other Iraqi forces "as one team, and we (achieved) this great victory," Ameri said.